Its trading volume averages $40bn a day, and its share of US dollar volumes has climbed from 25 per cent to 52 per cent since 1990. The New York Stock Exchange has lost out, accounting for 46 per cent of dollar trading, down from 73 per cent.
Margaret Kelly, head of marketing at Nasdaq International, said: "Nasdaq now trades more shares, worth more money, than any other market."
Average daily volume stands at almost one billion shares a day, she said, with a record high of 1.4 billion in April.
Nasdaq's rapid growth has been fuelled by its specialisation in high- technology stocks, whose share prices have surged during the bull market. Online trading over the Internet has also attracted investors to the market.
Recently Nasdaq announced it planned to start an evening trading session for its biggest stocks later in the year. The hugely successful retail broker Charles Schwab said 70 per cent of its customers would like to be able to trade when they returned home from work.
Nasdaq said yesterday that research conducted in London by Mori, the polling organisation, showed that, following its advertising campaign, name recognition of Nasdaq exceeded that of the NYSE, at 36 per cent versus 31 per cent.
However, both stock markets have come increasingly under threat from online private trading systems and electronic communications networks, such as Reuters' Instinet, which match individual buy and sell orders.
Ms Kelly was upbeat about Nasdaq's UK prospects. "There is real momentum building amongst British investors to research and trade in US stocks," she said.